The problem with short gamma

[nitro]

There is much to be learned from examples such as yours, but it needs to be considered far more deeply and no one has thought through what I mean in this thread (probably my fault for not being clear).

From Peter Carr. This is what I mean:

Uncertain Volatility

Of the paths UUUU and UDUD, which path do you think is
more volatile?

• To a probabilist equating the word “volatility” to quadratic
variation of returns, both paths have the same volatility.
• On the other hand, to a statistician who equates volatility to
the standard deviation of the terminal log price, the required
estimation of the mean implies that the reverting path UDUD
has more volatility than the trending path UUUU.
• On the other hand, to an ATM option writer who does not plan
to delta-hedge, the trending path UUUU has more volatility
than the reverting path UDUD. This writer equates the word
“volatility” to the ATM implied to charge initially.
• On the other hand, to an ATM option writer who does plan
to delta-hedge, the reverting path UDUD has higher volatility
than the trending path UUUU. Again, equating the word
volatility to the initial ATM implied, this writer knows that
vega and gamma are more negative along the mean-reverting
path than the trending path. Forgetting the tree, these greeks
become relevant when one is uncertain about the magnitude
of squared returns and the possibility of crashes.
• Of course, an ATM option buyer disagrees with the seller on
which path is more volatile and an OTM call trader disagrees
again.

Quote from JJacksET4:

What I find interesting is that it seems like volatility can be low, but prices can move strongly over a period of time. Like I mentioned in an earlier thread, GS has moved from 155 range to 175 range so quietly few people noticed and I think IV and HV are real low.

It seems like there should be better way to measure change and not just volatility. For a quick example, if a stock did this in the last 7 trading days:
50
52
54
56
58
60
62
would you want to sell a 65 call for a low price just because the price isn't volatile?
I'm not sure if I'm explaining this correctly, but there is more to price movement then volatility.

Actually, Bernie Schaffer has an example like this in his book. Something like a strong uptrending stock was at $55 and a stock that went up and down quickly and was at $55 and that stock had way more premium, so it was fairly cheap to buy 55 strike calls on the stocks that was a strong uptrender. Interesting to think about anyway.

JJacksET4

 

[asiaprop]

of course they do. The new game in town, every failed stock day trader has overnight become an options expert, you did not notice that? Very soon I expect most bucket fx shops to also offer fx options. Look at Saxobank: Do you think that 15-20 pip spreads in even the most liquid option pairs deters some of those idiots from trading them? Promise people lottery like pay offs and you are guaranteed to have takers, from the beginning until the end of human kind.

Surprised?

Quote from nitro:

What is even funnier to me is, option volumes are going through the roof, with equity volumes going lower.

That means people are using options strictly for leverage.

 

[nitro]

Books tell you that the only unknown in options trading is volatility, and that if you can predict this better than others you will make money. That is a bunch of shit. Look at the above example from Peter Carr.

"Volatility" (the actual volatility you experience) depends on your hedging strategy, which in turn depends on the path dependency of the underlying.

There is no way to get around trading delta unless you have access to sophisticated instruments like hyper options or [co]variance swaps.

 

[asiaprop]

well, thats why a lot of professionals dont hedge greeks based on implied vols but on other measures of vol, a basic example being realized vols. It creates more variability in your p&l curve but makes your final payoff a lot more predictable. Just my 2 cents...

Quote from nitro:

I just realized something. If it is true that the presence of return autocorrelation affects the volatility and expected value of asset price and BS therefore mis-prices vola [which in turn mis-prices delta/gamma], why not adjust the model such that we make vola functions of time to expiration and correlation coefficient, ρ? In this new framework the asset price volatility can no longer be expressed as σ^2t where σ^2 is the variance of asset price returns. Adding ρ would bias asset price volatility proportional to the autocorrelation coefficient as well as time.

Is is as "simple" as adding ρ to this term, σ^2 ρt ?

 

[RedEyeFly]

Vols are independently unpredictable. You can plan your derivative position to respond to a change in vol however you like, but the amount of implied vol stuffed in to BS or whatever pricing equation used is a variable without supply:demand, or any other market force. It's simply a stat.

For options, you can have expectations regarding how various strikes will react to each other as vol change hits the market.

Quants normally allow volatility a wide berth, and rightly so.

 

[asiaprop]

+1 better explanation than mine above.

It pays to understand to what vol large market making desks hedge and how their "end product" is parametrized. Not in order to be able to replicate or time their moves but to understand how your p/l evolves on delta hedged option strategies, on average being p/l= vega( sigma implied - sigma realized).

Quote from Martinghoul:

As I have mentioned to you before, nitro, it's all been done already. The whole point of stoch vol models is to treat volatility as a random variable. How to parameterize its behavior is the million dollar question with a whole variety of possible answers. You pick whichever one suits your view.

 

[nitro]

Peter Carr
The definition of volatility is itself volatile.

 

[nitro]

Quote from asiaprop:

well, thats why a lot of professionals dont hedge greeks based on implied vols but on other measures of vol, a basic example being realized vols. It creates more variability in your p&l curve but makes your final payoff a lot more predictable. Just my 2 cents...

That doesn't address the issue.

 

[nitro]

Quote from Martinghoul:

As I have mentioned to you before, nitro, it's all been done already. The whole point of stoch vol models is to treat volatility as a random variable. How to parameterize its behavior is the million dollar question with a whole variety of possible answers. You pick whichever one suits your view.

I sort of mixed two issues into one and misled by mixing correct gamma/delta hedges when in fact it is all about when and how to hedge, period, not the amount of the hedge.

My point and beautifully exemplified by Carr is that depending on your position and how you hedge, you see different volatility, and you are back to trading the underlying. This is true even in model-free scenarios and has nothing to do with stochastic vols.

 

[nitro]

Quote from asiaprop:

...
It pays to understand to what vol large market making desks hedge and how their "end product" is parametrized. Not in order to be able to replicate or time their moves but to understand how your p/l evolves on delta hedged option strategies, on average being p/l= vega( sigma implied - sigma realized).

Even if I believe this could help (I have to think about it) AFAIK, there is no way to back that out from publicly available information. It may be possible to do with P/C ratios and open interest, but only in extremely crude form, imo.

The last equation is also something you see in books, but is also grossly incomplete. When and how you hedge is everything when combined with the path the underlying takes.